Closed form evaluations of some series comprising sums of exponentiated multiples of two-term and three-term Catalan number linear combinations

Hdl Handle:
http://hdl.handle.net/10545/620855
Title:
Closed form evaluations of some series comprising sums of exponentiated multiples of two-term and three-term Catalan number linear combinations
Authors:
Larcombe, Peter J.
Abstract:
Closed form evaluations of some infinite series comprising sums of exponentiated multiples of two-term and three-term Catalan number linear combinations are presented using three contrasting approaches. Known power series expansions of the trigonometric functions sin(4α) and sin(6α) each readily give a set of (four) results which are reformulated via a hypergeometric route and, additionally, using only the generating function for the Catalan sequence; the latter two methods are shown to be connected.
Affiliation:
University of Derby
Citation:
Larcombe, P. J. (2015) 'Closed form evaluations of some series comprising sums of exponentiated multiples of two-term and three-term Catalan number linear combinations', Fibonacci Quarterly, 53 (3)
Publisher:
The Fibonacci Association
Journal:
Fibonacci Quarterly
Issue Date:
Aug-2015
URI:
http://hdl.handle.net/10545/620855
Additional Links:
http://www.fq.math.ca/index.html; http://www.fq.math.ca/53-3.html
Type:
Article
Language:
en
ISSN:
0015-0517
Appears in Collections:
Department of Electronics, Computing & Maths

Full metadata record

DC FieldValue Language
dc.contributor.authorLarcombe, Peter J.en
dc.date.accessioned2016-11-15T12:26:00Z-
dc.date.available2016-11-15T12:26:00Z-
dc.date.issued2015-08-
dc.identifier.citationLarcombe, P. J. (2015) 'Closed form evaluations of some series comprising sums of exponentiated multiples of two-term and three-term Catalan number linear combinations', Fibonacci Quarterly, 53 (3)en
dc.identifier.issn0015-0517-
dc.identifier.urihttp://hdl.handle.net/10545/620855-
dc.description.abstractClosed form evaluations of some infinite series comprising sums of exponentiated multiples of two-term and three-term Catalan number linear combinations are presented using three contrasting approaches. Known power series expansions of the trigonometric functions sin(4α) and sin(6α) each readily give a set of (four) results which are reformulated via a hypergeometric route and, additionally, using only the generating function for the Catalan sequence; the latter two methods are shown to be connected.en
dc.language.isoenen
dc.publisherThe Fibonacci Associationen
dc.relation.urlhttp://www.fq.math.ca/index.htmlen
dc.relation.urlhttp://www.fq.math.ca/53-3.htmlen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.subjectDiscrete mathematicsen
dc.subjectApplied mathematicsen
dc.titleClosed form evaluations of some series comprising sums of exponentiated multiples of two-term and three-term Catalan number linear combinationsen
dc.typeArticleen
dc.contributor.departmentUniversity of Derbyen
dc.identifier.journalFibonacci Quarterlyen
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